Really poorly done wiring - many I've looked at have a spaghetti factory going on behind the dash and in the engine compartment.
Tack welded or (much worse) sheet metal screwed-in floor panels.
Seats bolted to the floor panels with no substantial backing metal under the floors for strength (yeah, like four 1/4"-20 bolts are going to hold the seats in in an impact?)
Poor routing of the fuel line/hose, especially in the rear, which allows contact abrasion and/or too close to exhaust pipes (causing vapor lock and worse).
Lack of a positive anchor point for front and rear ends of the steel gas line, allowing it to flap around, fatigue and, eventually, break.
Lack of a front body suspension bracket. This sits on top of the front torsion bar mounts just ahead of the fuel tank and holds up the nose of the car. Without it you get both fiberglass fracturing around/near the headlights and at the front bottom corner of the door frame.
The "Infamous CMC Butt Sag" caused, not so much by fatigue of the frame over time (which probably adds slightly to it) but more so by really poor assembly by the "factory" such that the body was just slapped onto the frame and the rear clip riveted to the rear portion of the frame without ever making the door gaps correct in the first place. Fix is to drill out 6-8 rivets holding the body to the rear frame, jack up the body til the door gaps are straight and even and rivet or bolt it back together.
Check for a wide-area bubble in the fiberglass between the engine cover and the top of the rear cowl - right where one might put a third brake light above the engine cover. At this age, it will never get any bigger but it sometimes looks a bit odd if you notice it. They're sometimes 16" across and 8" front to back. If the top cowl looks as if the line doesn't match the line across the engine cover (like it bulges slightly) then you can live with it or have it taken out and filled.
On the plus side......a lot of CMC's had the thickest fiberglass in the industry and, as a whole, are usually pretty good bodies. What detracts from a CMC is usually the build quality Which varied widely between (amateur) builders.